Summary: Vorlesungsskript Rechnergest˜ utztes Beweisen
Martin Hofmann
WS 2003/04
1 Introduction
Computer­aided theorem proving means to carry out mathematical proofs on a
computer whose job it is to check steps, to perform bookkeeping tasks and to
automate routine steps. Conducting a proof on a computer may be compared to
and has a lot in common with implementing an informally given algorithm or
model. For example, a number of details must be filled in and, more importantly,
mistakes and shortcomings of the high­level model are brought to the surface.
Computer­aided theorem proving has numerous applications in program and
hardware verification as well as prototype development. To a lesser, perhaps in­
creasing, degree it is used to aid the development of genuine mathematical proofs.
1.1 Course outline
In this course, we will get to know the computer­based theorem prover PVS
(pvs.csl.sri.com) along with its theoretical foundations and some ramifi­
cations thereof. Those are for instance
. Logical foundations: sequent calculus, set theory
. Expressive power: cut elimination
. Automation of equational reasoning: rewriting